Since its introduction, the integrability criterion of the Consistency Around the Cube (CAC) has been a source of many results in the classification of equations
defined on the square (quad-equations). The first results were obtained in [V. E. Adler, A. I. Bobenko and Y. B. Suris, Comm. Math. Phys., 233, 513-543, 2003] and then extended in [V. E. Adler, A. I. Bobenko, Yu. B. Suris, Funct. Anal. Appl., 43, 317, 2009] releasing some hypothesis. The final step in the classification of the CAC equations was done by Raphael Boll in his Ph. D. dissertation [R. Boll, Classification and Lagrangian structure of 3D consistent quad-equations, Ph. D. dissertation, 2012.]. We will show that all the new equations appearing in the classification of Boll have linear growth of the degrees of the iterates, therefore according to the Algebraic Entropy criterion [C. Viallet, arXiv:math-ph/0609043] these equations must be not only integrable, but also linearizable. We show in a concrete example how to obtain such linearization and we discuss how this in fact confirms the results of the Algebraic Entropy. We finally discuss a possible generalization of these kind of equations.
How to participate in this seminar:
1. Book your nearest ACE facility;
2. Notify the ACE contact person at the host institution (Darren Condon) to notify you will be participating.
No access to an ACE facility? Contact Maaike Wienk to arrange a temporary Visimeet licence for remote access (limited number of licences available – first come first serve)